CN113568051A - Transient electromagnetic auxiliary interpretation method based on mathematical statistics - Google Patents
Transient electromagnetic auxiliary interpretation method based on mathematical statistics Download PDFInfo
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- G01V3/00—Electric or magnetic prospecting or detecting; Measuring magnetic field characteristics of the earth, e.g. declination, deviation
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Abstract
The invention discloses a transient electromagnetic auxiliary interpretation method based on mathematical statistics, which is used for the field of electromagnetic exploration and comprises the following steps: s1, performing regression fitting of the data, and fitting and correcting the inversion apparent resistivity data based on linear, quadratic or cubic polynomial fitting; s2, comparing the fitting results of various regression equations with the original image, and selecting the regression fitting results suitable for each region for auxiliary explanation; s3, normal distribution analysis, wherein the normal distribution analysis is combined with hydrogeological data and past work experience, and the interval division value of the normal distribution is used as the reference basis for dividing relative water-rich areas in different water-bearing stratums to perform electric method auxiliary explanation; the invention corrects the data by using a regression fitting trend surface method, summarizes a method for judging and classifying abnormal numerical values in the electrical method data by using the normal distribution empirical rule of each work area by using the characteristics of normal distribution, reduces artificial interpretation errors and obtains a more scientific, objective and convincing conclusion.
Description
Technical Field
The invention relates to the field of electromagnetic exploration, in particular to a transient electromagnetic auxiliary interpretation method based on mathematical statistics.
Background
Transient electromagnetic exploration is greatly influenced by terrain and external electromagnetic interference in the construction process, although relevant production technical measures are adopted in the construction process, technical means such as filtering and correction are adopted in later-stage data processing, the influences cannot be eliminated, abnormal areas in interpretation results are mainly distributed near the interference range, abnormal value judgment of the whole area can be carried out only in a partitioning and grading mode, great trouble is brought to later-stage data interpretation, and interpretation precision is influenced.
In the qualitative and semi-quantitative interpretation process, the abnormal threshold of each target layer is generally determined according to the hydrogeological condition of an exploration area and the underground excavation current situation, but the hydrogeological condition in the exploration area in part of projects is less, the underground excavation work is not carried out, so that the qualitative and semi-quantitative interpretation has no relevant reference basis, and meanwhile, different technicians have different cognition on the exploration area, so that the interpretation results of different technicians in the area with less data have certain difference, the interpretation precision is low, and the reliability of the interpretation results is influenced.
Disclosure of Invention
The invention provides a transient electromagnetic auxiliary interpretation method based on mathematical statistics, which corrects data by using a regression fitting trend surface method, averages the numerical values of plane data, summarizes the normal distribution empirical rule of each work area by using the characteristics of normal distribution to judge and classify abnormal numerical values in electrical method data, is beneficial to judging and valuing the abnormal numerical values in data interpretation and reduces manual interpretation errors.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
the method comprises the following steps of S1, performing regression fitting of data, and fitting and correcting the inversion apparent resistivity data based on linear, quadratic or cubic polynomial fitting;
s2, comparing the fitting results of various regression equations with the original image, and selecting the regression fitting results suitable for each region for auxiliary explanation;
and S3, normal distribution analysis, wherein the normal distribution analysis is combined with hydrogeological data and past work experience, and interval segmentation values of the normal distribution are used as threshold values to divide the water-rich property into strong, medium and weak, so as to perform auxiliary explanation.
The invention is further improved in that: in step S1, two or more mathematical models are selected according to the correlation and the specific form of the original data, and used to approximate the relationship of quantitative variation between the variation amounts having the correlation, so as to perform overall estimation and analytical prediction of the data.
The invention is further improved in that: the mathematical model is more than two regression equations.
The invention is further improved in that: the regression equation includes a linear fitting formula, a quadratic polynomial fitting formula, and a cubic polynomial fitting formula.
The invention is further improved in that: the linear fitting formula is y =0.0132x +6.2272, and the quadratic polynomial fitting formula is y = -4E-05x2+0.1308X-75.059, the cubic polynomial is y = -1E-07X3+0.0005x2-0.6198x+267.49。
Due to the adoption of the technical scheme, the invention has the beneficial effects that:
the invention corrects the data by using a regression fitting trend surface method, so that the numerical value of the plane data is averaged, abnormal values in different areas on the plane can be judged by using the same standard, and the application effect is better particularly in a working area with larger span and serious interference.
The method for judging and classifying the abnormal values in the electrical law data by using the normal distribution characteristic can be summarized by using the normal distribution empirical rule of each work area, is suitable for quickly and objectively judging and taking the abnormal range in data interpretation so as to obtain a more scientific, more objective and more convincing conclusion, removes artificial factors and reduces the artificial interpretation error.
Drawings
FIG. 1 is a flow chart of the present invention.
FIG. 2 is a graph showing the linear, quadratic, cubic polynomial fitted trend lines and formula comparisons according to the present invention.
FIG. 3 is a diagram showing comparison between the fitting results of the original data and the quadratic polynomial and the cubic polynomial according to the present invention.
FIG. 4 is a sectional empirical schematic diagram of the values of the apparent resistivity of the low resistivity anomaly of the formations with different water-rich types.
Detailed Description
The present invention will be described in further detail with reference to the following examples:
a transient electromagnetic auxiliary interpretation method based on mathematical statistics is disclosed, as shown in FIGS. 1-4, and comprises the following steps: s1, performing regression fitting of the data, as shown in figure 2, and performing fitting correction on the inversion apparent resistivity data based on linear, quadratic or cubic polynomial fitting;
s2, comparing the fitting results of various regression equations with the original image, and selecting the regression fitting results suitable for each region for auxiliary explanation, as shown in FIG. 3;
s3, performing normal distribution analysis data statistics, performing strong, medium and weak water-richness division by combining normal distribution analysis with hydrogeological data and past work experience and using the interval division value of normal distribution as a threshold value to perform auxiliary explanation, as shown in FIG. 4.
The inversion apparent resistivity data of a certain mine in Shanxi is taken as an example for detailed description, the apparent resistivity is a parameter for reflecting the electrical change characteristics of the rock, and the greater the apparent resistivity is, the smaller the water-rich property is.
TABLE 1 comparison table of original data of K8 aquifer in Shanxi province and normal distribution of "rule of thumb" zone data
The isoline with apparent resistivity smaller than 70 omega m is taken as a dividing principle of the water-rich abnormal region, and the dividing value is closer to the mu-1 sigma dividing value through data statistical analysis; the apparent resistivity greater than 250 omega m is used as high-resistance abnormal region division, the numerical value is closer to the value of a mu +2 sigma division point, the data with the apparent resistivity greater than 350 omega m is less in the actual data processing explanation, the extreme value caused by the influence of interference can be judged, and the extreme value can be deleted. From the statistics, it can be seen that in the "rule of thumb" analysis, the result of the data segmentation value is close to the result of the abnormal interpretation in practice, and the result proves to have reference value for the interpretation.
In the table, the water-rich area with the dividing rule of 72.5 Ω · m is very verified, and can be quickly used for explanation. The above table, which is associated with the b normal strata in fig. 4, may serve as an aid to explanation.
As shown in fig. 2, ps is the actual value of the inversion, the linear fitting formula on the graph is y =0.0132X +6.2272, the quadratic polynomial fitting formula is y = -4E-05X2+0.1308X-75.059, and the cubic polynomial fitting formula is y = -1E-07X3+0.0005X2-0.6198X + 267.49.
And selecting various mathematical models according to the correlation relationship and the specific form of the original data, and using the mathematical models to approximately express the relationship of quantity change among the variable quantities of the correlation relationship so as to carry out overall estimation and analysis prediction of the data. And performing regression fitting on the inverted actual numerical values to form a linear fitting trend line, a quadratic polynomial fitting trend line and a cubic polynomial fitting trend line by a numerical calculation method.
FIG. 2 is a plot of a single point fit, except for the data after the single point fit. And figure 3 is a plot of data fitted to a number of points. In fig. 3, it can be seen from the original data chart that the south of the area 1 is seriously affected by the high-voltage line and the terrain, and if the south of the area 1 is divided according to the value-taking rule, the south of the area is interpreted as a water-rich area and does not accord with the geological rule.
As can be seen from the quadratic polynomial fitting result and the cubic polynomial fitting result in FIG. 3 after fitting by a mathematical method, although the position of a place without interference has some deviation and trend, the quadratic polynomial fitting result or the cubic polynomial fitting result can be selected to be more in line with the geological rule according to hydrological data and geological experience. The 1, 2, 3, 6, 7, 8 and 9 regions in the raw data of fig. 3 have approximately the same form as the second-order polynomial fitting result, and although the apparent resistivity value of the 4 region is greater than the threshold value of abnormal division, the 4 region shows that two high-resistance regions sandwich one low-resistance abnormal region, which can also be interpreted as a water-rich region in electrical prospecting. The 9 region and the 8 region in the cubic polynomial fitting result are connected into pieces, and have certain difference with the original data form, so the quadratic polynomial fitting result is more suitable for the use of example areas. Meanwhile, the large-area low-resistance abnormality of the region affected by the terrain and the high-voltage line in the south part of the area 1 in the original data is greatly reduced after being fitted by a mathematical method, and the geological rule is better met. Therefore, under the conditions of less data and stronger interference, the fitting results of various regression equations are compared with the original image, and regression fitting results suitable for each region can be selected for auxiliary explanation so as to reduce the influence of human factors and quickly and accurately obtain relatively objective, scientific and convincing conclusions.
As can be seen from FIG. 4, the water-rich region in the region where the apparent resistivity is high is relatively weak, and the water-rich region generally corresponds to the low-resistance abnormal region, so that only the region from μ -1 σ to μ -3 σ is focused, and the region from μ +1 σ to μ +1 σ is not focused. That is, apparent resistivity values greater than μ +1 σ (160.0 Ω · m) are high-resistivity regions, and are not referred to in the division of the aquifer into water-rich regions.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (5)
1. A transient electromagnetic auxiliary interpretation method based on mathematical statistics is characterized by comprising the following steps:
s1, performing regression fitting of the data, and fitting and correcting the inversion apparent resistivity data based on linear, quadratic or cubic polynomial fitting;
s2, comparing the fitting results of various regression equations with the original image, and selecting the regression fitting results suitable for each region for auxiliary explanation;
and S3, normal distribution analysis, wherein the normal distribution analysis is combined with hydrogeological data and past work experience, and interval segmentation values of the normal distribution are used as threshold values to divide the water-rich property into strong, medium and weak, so as to perform auxiliary explanation.
2. The transient electromagnetic auxiliary interpretation method based on mathematical statistics as claimed in claim 1, characterized in that: in step S1, two or more mathematical models are selected according to the correlation and the specific form of the original data, and used to approximate the relationship of quantitative variation between the variation amounts having the correlation, so as to perform overall estimation and analytical prediction of the data.
3. The transient electromagnetic auxiliary interpretation method based on mathematical statistics as claimed in claim 2, characterized in that: the mathematical model is more than two regression equations.
4. The transient electromagnetic auxiliary interpretation method based on mathematical statistics as claimed in claim 3, characterized in that: the regression equation includes a linear fitting formula, a quadratic polynomial fitting formula, and a cubic polynomial fitting formula.
5. The transient electromagnetic auxiliary interpretation method based on mathematical statistics as claimed in claim 4, characterized in that: the linear fitting formula is y =0.0132x +6.2272, and the quadratic polynomialThe fitting formula of the formula is y = -4E-05x2+0.1308X-75.059, the cubic polynomial is y = -1E-07X3+0.0005x2-0.6198x+267.49。
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